As defined by Rattay, in the article, “Analysis of models for extracellular fiber stimulation,” IEEE Transactions on Biomedical Engineering, Vol. 36, no. 2, p. 676, 1989, which is incorporated herein by reference, the activation function (AF) is the second spatial derivative of the electric potential along an axon. In the region where the activation function is positive, the axon depolarizes, and in the region where the activation function is negative, the axon hyperpolarizes. If the activation function is sufficiently positive, then the depolarization will cause the axon to generate an action potential; similarly, if the activation function is sufficiently negative, then local blocking of action potentials transmission occurs. The activation function depends on the current applied, as well as the geometry of the electrodes and of the axon.
For a given electrode geometry, the equation governing the electrical potential is:∇(σ∇U)=4πj, 
where U is the potential, σ is the conductance tensor specifying the conductance of the various materials (electrode housing, axon, intracellular fluid, etc.), and j is a scalar function representing the current source density specifying the locations of current injection. The activation function is found by solving this partial differential equation for U. If the axon is defined to lie in the z direction, then the activation function is:
  AF  =                              ∂          2                ⁢        U                    ∂                  z          2                      .  
In a simple, illustrative example of a point electrode located a distance d from the axis of an axon in a uniformly-conducting medium with conductance σ, the two equations above are solvable analytically, to yield:
      AF    =                            I                      e            ⁢                                                  ⁢            1                                    4          ⁢          πσ                    ·                                    2            ⁢                          z              2                                -                      d            2                                                (                                          z                2                            +                              d                2                                      )                    2.5                      ,
where Iel is the electrode current. It is seen that when σ and d are held constant, and for a constant positive Iel (to correspond to anodal current), the minimum value of the activation function is negative, and is attained at z=0, i.e., at the point on the nerve closest to the source of the anodal current. Thus, the most negative point on the activation function corresponds to the place on a nerve where hyperpolarization is maximized, namely at the point on the nerve closest to the anode.
Additionally, this equation predicts positive “lobes” for the activation function on either side of z=0, these positive lobes peaking in their values at a distance which is dependent on each of the other parameters in the equation. The positive values of the activation function correspond to areas of depolarization, a phenomenon typically associated with cathodic current, not anodal current. However, it has been shown that excess anodal current does indeed cause the generation of action potentials adjacent to the point on a nerve corresponding to z=0, and this phenomenon is therefore called the “virtual cathode effect.” (An analogous, but reverse phenomenon, the “virtual anode effect” exists responsive to excess cathodic stimulation.)
U.S. Pat. No. 6,684,105 to Cohen et al., which is assigned to the assignee of the present application and is incorporated herein by reference, describes apparatus comprising an electrode device adapted to be coupled to longitudinal nervous tissue of a subject, and a control unit adapted to drive the electrode device to apply to the nervous tissue a current which is capable of inducing action potentials that propagate in the nervous tissue in a first direction, so as to treat a condition. The control unit is further adapted to suppress action potentials from propagating in the nervous tissue in a second direction opposite to the first direction.
U.S. Pat. No. 6,230,061 to Hartung, which is incorporated herein by reference, describes an electrode arrangement for stimulating the heart by means of: (a) an implantable cardiac pacemaker, (b) a first electrode, coupled to a first output of the pacemaker via an intracardiac electrode line, and (c) a second electrode, for transmitting electrical stimulation pulses to the heart tissue, coupled to a second output of the pacemaker via the electrode line. The voltage pulses at the two electrodes have differing polarities relative to a third electrode. The first and second electrodes are arranged on the electrode line in such a way that the electrical dipole field which forms is distorted towards the stimulation point in such a way that a raised gradient above the stimulus threshold is formed there.
A number of patents and articles describe methods and devices for stimulating nerves to achieve a desired effect. Often these techniques include a design for an electrode or electrode cuff.
U.S. Pat. Nos. 4,608,985 to Crish et al. and 4,649,936 to Ungar et al., which are incorporated herein by reference, describe electrode cuffs for selectively blocking orthodromic action potentials passing along a nerve trunk, in a manner intended to avoid causing nerve damage.
PCT Patent Publication WO 01/10375 to Felsen et al., which is incorporated herein by reference, describes apparatus for modifying the electrical behavior of nervous tissue. Electrical energy is applied with an electrode to a nerve in order to selectively inhibit propagation of an action potential.
U.S. Pat. No. 5,755,750 to Petruska et al., which is incorporated herein by reference, describes techniques for selectively blocking different size fibers of a nerve by applying direct electric current between an anode and a cathode that is larger than the anode.
U.S. Pat. No. 5,487,756 to Kallesoe et al., which is incorporated herein by reference, describes an implantable cuff having a closure comprising a set of small interdigitated tubes lying along the edges of a longitudinal slit opening in the cuff. A rod-like locking member is inserted through the interdigitated tubes to lock the cuff closed. A flexible flap attached to the inside of the cuff is described as electrically and mechanically isolating the interior of the cuff from the exterior.
U.S. Pat. No. 5,824,027 Hoffer et al., which is incorporated herein by reference, describes a nerve cuff having one or more sets of electrodes for selectively recording electrical activity in a nerve or for selectively stimulating regions of the nerve. Each set of electrodes is located in a longitudinally-extending chamber between a pair of longitudinal ridges which project into the bore of the nerve cuff. The ridges are electrically insulating and serve to improve the selectivity of the nerve cuff. The ridges seal against an outer surface of the nerve without penetrating the nerve. In an embodiment, circumferential end sealing ridges extend around the bore at each end of the longitudinal ridges, and are described as enhancing the electrical and/or fluid isolation between different ones of the longitudinally-extending chambers.
U.S. Pat. No. 4,628,942 to Sweeney et al., which is incorporated herein by reference, describes an annular electrode cuff positioned around a nerve trunk for imposing electrical signals on to the nerve trunk for the purpose of generating unidirectionally propagated action potentials. The electrode cuff includes an annular cathode having a circular passage therethrough of a first diameter. An annular anode has a larger circular passage therethrough of a second diameter, which second diameter is about 1.2 to 3.0 times the first diameter. A non-conductive sheath extends around the anode, cathode, and nerve trunk. The anode and cathode are placed asymmetrically to one side of the non-conductive sheath.
U.S. Pat. No. 5,634,462 to Tyler et al., which is incorporated herein by reference, describes a corrugated sheet of non-conductive biocompatible material that is biased to circumferentially contract around a nerve or other body tissue. Conductive members are disposed on inwardly projecting portions of the corrugated sheet formed into a cylinder around the nerve. The conductive segments are electrically conductive for applying or recording electrical impulses or fluid conductive for infusing medications or draining fluids from the nerve. The corrugated sheet, when wrapped around a nerve, is self-biased to slowly controllably contract to its original size.
U.S. Pat. No. 6,456,866 to Tyler et al., which is incorporated herein by reference, describes a flat interface nerve electrode having a plurality of conductive elements embedded in a non-conductive cuff structure, which acts to gently and non-evasively redefine the geometry of a nerve through the application of a force so as to apply pressure to a nerve in a defined range.
U.S. Pat. No. 4,602,624 to Naples et al., which is incorporated herein by reference, describes a self-curling sheet of non-conductive material that is biased to curl into a tight spiral. A cut out is removed from one corner of the sheet such that, when the sheet spirals, a passage defined axially therethrough has one portion with a smaller diameter and another portion with a larger diameter. A pair of conductive strips are disposed on the self-curling sheet such that one extends peripherally around each of the larger and smaller diameter regions of the passage therethrough. The conductive segments may be electrically conductive for applying electrical impulses or fluid conductive for infusing medications. In use, a first edge of the self-curling sheet is disposed adjacent a nerve trunk which is to receive the cuff therearound. The self-curling sheet is controllably permitted to curl around the nerve forming an annular cuff therearound.
U.S. Pat. No. 6,600,956 to Maschino et al., which is incorporated herein by reference, describes an electrode assembly to be installed on a patient's nerve. The assembly has a thin, flexible, electrically insulating circumneural carrier with a split circumferential configuration longitudinally attached to a lead at the distal end thereof. The carrier possesses circumferential resiliency and has at least one flexible, elastic electrode secured to the underside thereof and electrically connected to an electrical conductor in said lead. A fastener serves to close the split configuration of the carrier to prevent separation from the nerve after installation of the electrode assembly onto the nerve. Tear-away webbing secured to adjacent serpentine segments of the lead near the carrier enables the lead to lengthen with patient movements.
U.S. Pat. No. 5,199,430 to Fang et al., which is incorporated herein by reference, describes cuff electrodes that are implanted around sacral ventral root nerve trunks.
U.S. Pat. No. 5,423,872 to Cigaina, which is incorporated herein by reference, describes a process for treating obesity and syndromes related to motor disorders of the stomach of a patient. The process consists of artificially altering, by means of sequential electrical pulses and for preset periods of time, the natural gastric motility of the patient to prevent emptying or to slow down gastric transit. The '872 patent describes an electrocatheter adapted to be coupled to a portion of the stomach. A portion of the electrocatheter has a rough surface for producing a fibrous reaction of the gastric serosa, in order to contribute to the firmness of the anchoring.
U.S. Pat. No. 5,282,468 to Klepinski, which is incorporated herein by reference, describes an implantable neural electrode.
U.S. Pat. No. 4,535,785 to van den Honert et al., which is incorporated herein by reference, describes implantable electronic apparatus.
U.S. Pat. No. 5,215,086 to Terry et al., which is incorporated herein by reference, describes a method for applying electrical stimulation to treat migraine headaches.
U.S. Pat. No. 4,573,481 to Bullara, which is incorporated herein by reference, describes an implantable helical electrode assembly, configured to fit around a nerve, for electrically triggering or measuring an action potential or for blocking conduction in nerve tissue. A tissue-contacting surface of each electrode is roughened to increase the electrode surface area.
U.S. Pat. No. 6,341,236 to Osorio et al., which is incorporated herein by reference, describes techniques for electrically stimulating the vagus nerve to treat epilepsy with minimized or no effect on the heart. Treatment is carried out by an implantable signal generator, one or more implantable electrodes for electrically stimulating a predetermined stimulation site of the vagus nerve, and a sensor for sensing characteristics of the heart such as a heart rate. The heart rate information from the sensor can be used to determine whether the vagus nerve stimulation is adversely affecting the heart. Once threshold parameters are met, the vagus nerve stimulation may be stopped or adjusted. In an alternative embodiment, a modified pacemaker is used to maintain the heart in desired conditions during the vagus nerve stimulation. In yet another embodiment, a modified pacemaker having circuitry that determines whether a vagus nerve is being stimulated is used. In the event that the vagus nerve is being stimulated, the modified pacemaker may control the heart to maintain it within desired conditions during the vagus nerve stimulation.
The following articles, which are incorporated herein by reference, may be of interest:    Ungar I J et al., “Generation of unidirectionally propagating action potentials using a monopolar electrode cuff,” Annals of Biomedical Engineering, 14:437-450 (1986)    Sweeney J D et al., “An asymmetric two electrode cuff for generation of unidirectionally propagated action potentials,” IEEE Transactions on Biomedical Engineering, vol. BME-33(6) (1986)    Sweeney J D et al., “A nerve cuff technique for selective excitation of peripheral nerve trunk regions,” IEEE Transactions on Biomedical Engineering, 37(7) (1990)    Naples G G et al., “A spiral nerve cuff electrode for peripheral nerve stimulation,” by IEEE Transactions on Biomedical Engineering, 35(11) (1988)    van den Honert C et al., “Generation of unidirectionally propagated action potentials in a peripheral nerve by brief stimuli,” Science, 206:1311-1312 (1979)    van den Honert C et al., “A technique for collision block of peripheral nerve: Single stimulus analysis,” MP-11, IEEE Trans. Biomed. Eng. 28:373-378 (1981)    van den Honert C et al., “A technique for collision block of peripheral nerve: Frequency dependence,” MP-12, IEEE Trans. Biomed. Eng. 28:379-382 (1981)    Rijkhoff N J et al., “Acute animal studies on the use of anodal block to reduce urethral resistance in sacral root stimulation,” IEEE Transactions on Rehabilitation Engineering, 2(2):92 (1994)    Mushahwar V K et al., “Muscle recruitment through electrical stimulation of the lumbo-sacral spinal cord,” IEEE Trans Rehabil Eng, 8(1):22-9 (2000)    Deurloo K E et al., “Transverse tripolar stimulation of peripheral nerve: a modelling study of spatial selectivity,” Med Biol Eng Comput, 36(1):66-74 (1998)    Tarver W B et al., “Clinical experience with a helical bipolar stimulating lead,” Pace, Vol. 15, October, Part II (1992)    Hoffer J A et al., “How to use nerve cuffs to stimulate, record or modulate neural activity,” in Neural Prostheses for Restoration of Sensory and Motor Function, Chapin J K et al. (Eds.), CRC Press (1st edition, 2000)
In physiological muscle contraction, nerve fibers are recruited in the order of increasing size, from smaller-diameter fibers to progressively larger-diameter fibers. In contrast, artificial electrical stimulation of nerves using standard techniques recruits fibers in a larger- to smaller-diameter order, because larger-diameter fibers have a lower excitation threshold. This unnatural recruitment order causes muscle fatigue and poor force gradation. Techniques have been explored to mimic the natural order of recruitment when performing artificial stimulation of nerves to stimulate muscles.
Fitzpatrick et al., in “A nerve cuff design for the selective activation and blocking of myelinated nerve fibers,” Ann. Conf. of the IEEE Eng. in Medicine and Biology Soc, 13(2), 906 (1991), which is incorporated herein by reference, describe a tripolar electrode used for muscle control. The electrode includes a central cathode flanked on its opposite sides by two anodes. The central cathode generates action potentials in the motor nerve fiber by cathodic stimulation. One of the anodes produces a complete anodal block in one direction so that the action potential produced by the cathode is unidirectional. The other anode produces a selective anodal block to permit passage of the action potential in the opposite direction through selected motor nerve fibers to produce the desired muscle stimulation or suppression.
The following articles, which are incorporated herein by reference, may be of interest:    Rijkhoff N J et al., “Orderly recruitment of motoneurons in an acute rabbit model,” Ann. Conf. of the IEEE Eng., Medicine and Biology Soc., 20(5):2564 (1998)    Rijkhoff N J et al., “Selective stimulation of small diameter nerve fibers in a mixed bundle,” Proceedings of the Annual Project Meeting Sensations/Neuros and Mid-Term Review Meeting on the TMR-Network Neuros, Apr. 21-23, 1999, pp. 20-21 (1999)    Baratta R et al., “Orderly stimulation of skeletal muscle motor units with tripolar nerve cuff electrode,” IEEE Transactions on Biomedical Engineering, 36(8):836-43 (1989)
The following articles, which are incorporated herein by reference, describe techniques using point electrodes to selectively excite peripheral nerve fibers distant from an electrode without exciting nerve fibers close to the electrode:    Grill W M et al., “Inversion of the current-distance relationship by transient depolarization,” IEEE Trans Biomed Eng, 44(1):1-9 (1997)    Goodall E V et al., “Position-selective activation of peripheral nerve fibers with a cuff electrode,” IEEE Trans Biomed Eng, 43(8):851-6 (1996)    Veraart C et al., “Selective control of muscle activation with a multipolar nerve cuff electrode,” IEEE Trans Biomed Eng, 40(7):640-53 (1993)